This introductory Chapter presents the concepts that lie at the basis of Synthetic Biology, a new branch of Life Sciences also referred to as Life Engineering. Synthetic Biology aims at modifying living cells in such a way that they can carry out precise tasks. Possible applications range from biofuel production to drug synthesis, from cancer cell detection to removal of environmental pollutants. The main artefacts of Synthetic Biology are DNA circuits where sequences of DNA interact by exchanging proteins or RNA molecules. Importantly, circuit implementation in the wet-lab should be model-driven i.e. genetic networks should be associated with mathematical models. Modeling permits to simulate and evaluate circuit performance in silico before their actual realization in vivo.